Question
How many divisors does the number 5040
have?Solution
First, find the prime factorization of 5040: 5040 ÷ 2 = 2520 2520 ÷ 2 = 1260 1260 ÷ 2 = 630 630 ÷ 2 = 315 315 ÷ 3 = 105 105 ÷ 3 = 35 35 ÷ 5 = 7 So, the prime factorization of 5040 is: 5040 = 2⁴ × 3² × 5 × 7. The formula for the number of divisors is: (Number of divisors) = (Exponent of 2 + 1)(Exponent of 3 + 1)(Exponent of 5 + 1)(Exponent of 7 + 1). Therefore, the number of divisors = (4 + 1)(2 + 1)(1 + 1)(1 + 1) = 5 × 3 × 2 × 2 = 60. Correct option: e
Statements:
P < Q < R < S ≤ B < H; S > N ≥ Y
Conclusions:
I) P < Y
II) R ≥ N
In the question, assuming the given statements to be true, find which of the conclusion (s) among given three conclusions is/are definitely true and the...
Statements: P ≥ Q ≥ R = S, Q ≥ T > U ≥ V
Conclusion:
I. P ≥ V
II. P > V
Statements: J < K; L = M; K >N ≥ L
Conclusions:
I. J < L
II. N = M
Statements: M = N ≤ P = C > G, D ≥ M > T = F
Conclusion:
I. D ≥ N
II. N > F
III. F < P
Statements: A ≥ B ≥ Y = Z = M ≥ N ≤ E ≤ F = J
Conclusions:
I. F > Z
II. J ≤ Y
Which of the following expression symbols should replace the question mark(?) in the given expressions to make the expression C ≥ E as well as D > M d...
Statement: M < N; L ≥ U; L ≥ Q; U > N ≥ T
Conclusion:
I. N > Q
II. Q > T
Statements: X < H = U ≤ I < N = M, M > B ≥ V
Conclusions:
I. I > V
II. U ≥ MStatement: D > C > U < K > E > N < A
Conclusion:
I. D > N
II. D > A
